[72.07] A Moment Method for Cosmological Reionization - Single Point Source Case

P. Paschos (UIUC), M. L. Norman, J. Bordner (UCSD)

The epoch of the Universe's reionization begins at redshifts
z ~10 due to the expansion of ionization fronts
(IFs) from individual point sources and the subsequent
ionizing radiation emanating from the diffuse gas.

We have developed numerical methods, that use a multigrid
refinement solver (MGMPI), to solve the moment equations of
such radiation field for the energy density evolution in 3D.
Our methods make use of two approximations: Flux-limited
diffusion, for the diffuse component of the UV field and an
Eddington factor scheme, for point source radiation. In
order to test the results of the above methods, we have
focused on the case of a single point source. In spherical
coordinates the radial propagation of the radiative flux
vector is determined by the Eddington factor which in this
case is: frr=1 and fij=0 if (ij) \neq (rr). We
use a modified set of moment equations in spherical
coordinates from Mihalas & Mihalas (1984) to solve for the
energy density due to the point source, ignoring
recombination processes. These equations are then
transformed to 3D Cartesian coordinates for general
cosmological applications. The modification adds a time
derivative of the energy density in the zeroth moment
equation.

We have tested our method in the case of a homogeneous
medium, by comparing the position of the ionization front
with that calculated from the analytic approximation of an
expanding Strömgen sphere in a single species gas (HI).
The result shows that we are able to reproduce the correct
rate of expansion. The method is then tested in the case of
a non-evolving cosmological density distribution volume, to
determine whether it can handle density fluctuations. We
demonstrate that the ionization front propagates slower in
the opaque cores and filaments than in the voids, giving
rise to a complex distribution for the UV field. Finally we
demonstrate the effect of shadowing from an opaque Gaussian
overdensity.

This research is supported by NSF grant AST=9803137.
Calculations were carried out on supercomputers at the NCSA.